In [1]}, Morgenstern presented for every prime power \(q\) , infinitely many groups \(G_i = PGL_2(q^i)\)  or \(G_i = PSL_2(q^i)\)  each with a symmetric set \(B_i\)  of \(q+1\)  generators such that \(\mbox{Cay}(G_i,B_i)\)  are Ramanujan, i.e., \(\lambda (\mbox{Cay}(G_i,B_i))\leqslant \frac{2\sqrt{q}}{q+1}\) .
